Approaches exist in the industry for fault and salt body detection based on the premise that seismic faulting and salt introduce discontinuities in the seismic horizons. Several seismic attributes (e.g., chaos, coherence, variance, curvature, and Sobel filter attributes, etc.) have been used to enhance this discontinuity. Subsequent to the enhancement, the structures are extracted and compared to the original seismic data for quality control.
The Sobel operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the opposite of the gradient of the image intensity function. At each point in the image, the result of the Sobel operator is either the corresponding opposite of the gradient vector or the norm of this vector. The Sobel operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical directions and is therefore relatively inexpensive in terms of computations. On the other hand, the opposite of the gradient approximation that it produces is relatively crude, in particular for high frequency variations in the image. Mathematically, the Sobel operator uses two 3×3 kernels which are convolved with the original image to calculate approximations of the derivatives—one for horizontal changes, and one for vertical. If A represents the source image, and Gx and Gy represent two images which at each point contain the horizontal and vertical derivative approximations, the two dimensional Sobel operators are shown in a 3 by 3 matrix form as follows:
      G    s    =                    [                                                            -                1                                                    0                                                      +                1                                                                                        -                2                                                    0                                                      +                2                                                                                        -                1                                                    0                                                      +                1                                                    ]            *      A      ⁢                          ⁢      and      ⁢                          ⁢              G        y              =                  [                                                            -                1                                                                    -                2                                                                    -                1                                                                        0                                      0                                      0                                                                          +                1                                                                    +                2                                                                    +                1                                                    ]            *      A      where * denotes the 2-dimensional convolution operation.